Mathematical Sciences: Artinian Rings

数学科学：阿天环

• 批准号: 8807043
• 负责人: Birge Huisgen-Zimmermann
• 金额: --
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8807043&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Artinian; Rings

This project is concerned with various aspects of artinian rings. In particular, homological properties and decompositions of modules will be examined. Under the first heading, the goals are to establish further steps towards a confirmation of the Nakayama Conjecture and the Finitistic Dimension Conjecture and a solution to the Cartan Determinant Problem. In the second category, the proposer aims at the problem of whether the rings, all of whose left modules are direct sums of finitely generated modules, are of finite representation type. The research is in the general area of ring theory. A ring is an algebraic structure having both an addition and a multiplication. These objects arise naturally and are important in many areas of mathematics and physics.

这个项目涉及到阿丁环的各个方面。特别地，我们将研究模的同调性质和分解。在第一个标题下，目标是建立进一步的步骤，以证实Nakayama猜想和F初始维度猜想，并解决Cartan行列式问题。在第二类中，作者研究了左模都是有限生成模直和的环是否为有限表示型环的问题。这项研究属于环论的一般领域。环是既有加法又有乘法的代数结构。这些物体是自然产生的，在数学和物理的许多领域都很重要。